A parcel of mass 5kg lies or a rough plane inclined at an angle (alpha) to the horizontal, where tan (alpha) = 3/4. The parcel is held in equilibrium by the action of a horizontal force of magnitude 20N. The force acts in a vertical plane through a line of greatest slope of the plane. The parcel is on the point of sliding down the plane.

(Original post by sr2123)
A parcel of mass 5kg lies or a rough plane inclined at an angle (alpha) to the horizontal, where tan (alpha) = 3/4. The parcel is held in equilibrium by the action of a horizontal force of magnitude 20N. The force acts in a vertical plane through a line of greatest slope of the plane. The parcel is on the point of sliding down the plane.

(Original post by sr2123)
A parcel of mass 5kg lies or a rough plane inclined at an angle (alpha) to the horizontal, where tan (alpha) = 3/4. The parcel is held in equilibrium by the action of a horizontal force of magnitude 20N. The force acts in a vertical plane through a line of greatest slope of the plane. The parcel is on the point of sliding down the plane.

a) Find the coefficient of friction between the parcel and the plane.

Draw a diagram with everything you know so far. (include friction)

Hints:

Spoiler:

Show

To label the angles, work out what cos(alpha) and sin(alpha) are using the value of tan(alpha). If you're stuck, try drawing a right angled triangle with opposite side=3 and adjacent side=4.

Spoiler:

Show

Resolve the forces parallel and perpendicular to the surface to get an equation for R (the normal reaction).

As the particle is in equilibrium, what does this tell you about f=ma=?

Spoiler:

Show

0

Spoiler:

Show

What does the fact that the particle is on the point of sliding down the plane tell you about the frictional force F?